What is inductance?

Inductance is an electrical term related to conductor or inductor. Inductance is the property or capability of a conductor to oppose the change of flow of current through a particular circuit. The term inductance is from the inductor. The symbol L denotes inductance, and the unit of inductance is Henry (H). Inductance is generally a ratio of voltage and rate of change in current (Ampere). In practice, every conductor has an inductance property.

What is a transmission line?

Transmission lines are lines used to transmit something like signals. In terms of core electrical, transmission lines are the cables or specialized cables used to transmit high voltage power from one point to another (example, point P to point Q). Transmission lines are used to transfer high power over a long distance.

What is the inductance of a transmission line?

When power is transferred through a transmission line, many parameters interrupt them, like capacitance, inductance, resistance, etc. One of them is inductance. According to the Faraday law, the magnetic flux starts to generate when the current passes through the conductor. As the current varies, the generated flux also varies, resulting in an induced EMF (voltage or potential). This EMF that is induced during this process is because of inductance.

Parts of linking flux

Parts of linking flux within the conductor:

• Internal flux
• External flux

Internal flux

Internal flux is generally induced because of the flow of current through the conductor.

External flux

External flux is produced by two currents, one of it is current and another is the conductor placed near it. External flux is produced around the conductor.

Reason behind the inductance in a transmission line

The transmission lines transmit high power or high voltage and high current, which are alternating in nature. High alternating magnetic flux will generate when high AC passes through the conductor. This flux will form a linkage with the other flux generated by another conductor parallel to it. Flux linkage is both internally and externally. The ratio of flux linkage and the current cause inductance at this position.

The expression for the inductance is given by:

$L=\frac{\varphi }{I}$

Here, L is the inductance, $\varphi$ is the flux linkage and I is the current.

If the coil has N number of the turns, then:

$\mathrm{Inductance}=\frac{N\varphi }{I}$

In the transmission line the number of coils is 1. The flux linkage is is denoted by $\lambda$.

Calculation the inductance of a single conductor

There are two types of flux, i.e., internal flux and external flux. Here, the inductance is asked only for a single conductor, so it only acquires the internal magnetic flux offered by the current of the conductor.

Assume the dimensions of the conductor as follows:

The length of the conductor is L, the current is I, the radius is R, and the internal variable radius is r.

The ratio between the areas to the internal variable radius and the original radius is:

$\frac{I_r}{I}=\frac{\mathrm{\pi }{r}^2}{\pi R^2}$

Rearrange the above terms, we get:

$I_r=\frac{\mathrm{\pi }{r}^2}{\pi R^2}I$

The expression for the magnetic flux is $B={\mu }_0{H}_r$               ....... (1)

H is the magnetizing force.

The expression for the flux linkage is given as:

$$\begin{gathered} d\lambda =\frac{I_r}{I}d\varphi \\ d\lambda =\frac{\pi r^2}{\pi R^2}d\varphi \end{gathered}$$

For original length, we have:

$$\begin{gathered} \lambda ={\int }_0^{R}d\lambda \\ \lambda =\frac{{\mu }_0}{8\pi }I \end{gathered}$$

The internal inductance is given by the following:

$$\begin{gathered} L_{internal}=\frac{\lambda }{I} \\ {L}_{internal}=\frac{{\mu }_0}{8\pi } \end{gathered}$$

Types of transmission cables

The different types of transmission cable line are-

• Balanced two-wire
• Co-axial cable
• Waveguide
• Microstrip
• Fiber optics

Type of wire is used in transmission

We use various types of wire in high-power transmission, But mainly in open long transmission lines, stranded wire or stranded transmission wire are used.

Stranded wire is defined as a wire formed by two or more types of material in which the materials have different types of properties, such as stability, strength, conductivity, etc.

Types of transmission on the basis of phase and line

Types of transmission on the basis of phase and wire:

• Single-phase two-wire line
• Symmetrical three-phase three-wire line
• Unsymmetrical three-phase three-wire line

Two-wire single-phase line

This acquires two wires in a single phase with its dimensions of wire. Both the wires have their flux linkage. Assume two conductors A and B.

Flux linkage of conductor A:

$$\begin{gathered} {\lambda }_A=2\times {10}^{-7}\left[I_A \ln \frac{1}{D_{aa}}+I_B\frac{1}{D_{AB}}\right] \\ {\lambda }_A=2\times {10}^{-7}\left[I \ln \frac{D}{r}\right] \end{gathered}$$

Flux linkage of conductor B:

${\lambda }_B=2\times {10}^{-7}\left[I \ln \frac{D}{r}\right]$

Inductance (L) = inductance of conductor A= inductance of conductor B.

$L=L_A=L_B={\lambda }_B=2\times {10}^{-7}\left[\ln \frac{D}{r}\right]$

Symmetrical three-phase three-wire lines

In this type of arrangement, the wire or conductor is arranged at an angle of 60 degrees from each other with equal distance between them. Three wires form it.

The inductance of all three wires is the same, i.e.,

$L=L_A=L_B=L_C=2\times {10}^{-7}\left[\ln \frac{D}{r}\right]$

Here, L the inductance of a symmetrical three-phase three-wire system is the same as a single-phase two-wire system.

Unsymmetrical three-phase three-wire lines

In this type of arrangement, the three conductors or wires are not in a symmetric position which means the angle between them is not exactly 60 degrees from each other and has an unequal distance between them. It is used in operation because this arrangement is cheaper and easy to design.

The inductance of conductor A with reference to the conductor B and conductor C:

$L_A=2\times {10}^{-7}\left[\ln \frac{{\left(D_{12}{D}_{23}{D}_{31}\right)}^{\frac{1}{3}}}{r}\right]=L_B=L_C$

Here, D represents the distance between conductors.

Role of inductance in a transmission line

The inductance induced in the transmission line reduces the Ferranti effect.

When the transmission lines are operated on no-load or have a very low load, in this condition, the voltage at the receiving end is slightly greater than the sending end voltage. This effect is known as the Ferranti effect. To get rid of this effect, inductance induced in the transmission line helps to reduce the Ferranti effect.

Common Mistakes

It is necessary to know the difference between transmission lines and transmission cables.

Context and Applications

This is a very interesting and important topic which is useful in

• Bachelor of Technology in Electrical and Electronics Engineering
• Masters of Technology in Electrical Engineering

Related Concepts

• Insulators
• Circuit breaker
• Capacitance in transmission line

Practice Problems

Q1. Which one is not the parameter of a transmission line?

1. Capacitance
2. Inductance
3. Resistance
4. Impedance

Correct Option: (d)

Explanation: Impedance is a collective of all capacitance, inductance, and resistance.

Q2. Which condition is responsible for the Ferranti effect?

1. No load
2. Heavy load
3. Both
4. None of the above

Correct Option: (a)

Explanation: No load is responsible for the Ferranti effect.

Q3. Which parameter is required to have a symmetric transmission arrangement?

1. Resistance
2. Weight of the wire
3. Distance between the wires or phase
4. Material

Correct option: (c)

Explanation: It is essential to have an equal distance between all the phases to have a symmetric arrangement. If the distance between them is not equal, it comes in the category of unsymmetric.

Q4. Why do we use an overhead transmission line?

1. High current
2. High voltage
3. High inductance
4. Both (a) and (b)

Correct option: (d)

Explanation: Due to high current and high voltage, the overhead transmission line safeguards from the fault.

Q5. Which is not a content of a transmission line?

1. High voltage
2. High current
3. Inductance
4. Stranded wire

Correct option: (d)

Explanation: Stranded wire is not the content of a transmission line. It is a type of wire.